(1) Field of the Invention
The present invention relates to a method for the systematic prediction of stable high speed cutting parameters for machining titanium.
(2) Description of Related Art
Titanium alloys are used extensively in manufacturing helicopter components because of their excellent combination of high specific strength, which is maintained at elevated temperature, high resistance to corrosion, fracture resistance characteristics and extensive ductility, especially at high strain rates. Despite the excellent properties of titanium alloys, their machinability is generally considered poor due to the following inherent properties. First, the high strength maintained at elevated temperatures with a low modulus of elasticity impairs the machinability of titanium. Second, large amounts of heat are generated at the tool/workpiece interface adversely affecting the tool life because titanium alloys have thermal conductivity 13 times less than aluminum.
Third, machining of titanium produces typically shear-banded (segmented) chips due to poor thermal properties. These chips cause a sudden force fluctuation from a peak value to a minimum value. The rapid force fluctuation causes a hammering on the tool face at the tool tip in the vicinity of cutting. This phenomenon accelerates the tool chipping process as the cutting speed increases and reduces tool life to a fraction of a second.
Fourth, the segmented chips roll onto the tool face and have a short time of non-sliding contact. During machining the low thermal conductivity and high strength of titanium, alloys create high temperatures leading to high rates of tool wear.
Lastly, titanium is very chemically reactive, and has the tendency to weld to the cutting tool during machining, which leads to chipping and premature failure.
An existing method for controlling the tool chip interfacial temperature consists of a high-pressure coolant jet applied at the tool-chip interface. The high-pressure coolant is delivered through internal coolant passages and an array of discrete nozzles that eject the coolant onto the cutting edge at a predetermined mass flow rate and impingement pressure.
Yet another method for controlling the tool chip interfacial temperature consists of a high-pressure coolant jet applied at the tool-chip interface. A thermal-mechanical High Speed Machining (HSM) model is used to predict the interfacial temperature as a function of cutting speed, coolant flow rate, and coolant application angle. Based on the predicted temperature, the optimal integral nozzle configuration is designed. The nozzle shape is optimized through a definite element model for predicting interfacial temperature isotherms with the objective of minimizing their values.
Model predictions and experimental results show that the shaped nozzle creates a correspondingly shaped jet, which is more effective at removing heat from the tool-chip interface, thereby reducing the tool chip interface temperature. Although the high-pressure coolant applications evacuate the chips very efficiently and reduce the tool temperature, which allows the increase in the cutting speed and consequently the feed rate 10 times, tool life is very low. The main mechanism of tool failure is chipping. The fluctuation of the cutting forces due to chip segmentations is one of the main reasons for this chipping. High rigidity of machine tool, use of high feed, and low rake angle can mitigate tool chipping. The segment spacing of the chip is equal to the feed (or uncut chip thickness) and is governed by the rake angle. Increasing the segment spacing reduces the frequency of impact and increases the area of contact so that the forces will be less concentrated on the tool tip.
This solution cannot be generalized for any tool/workpiece/fixture system. In many applications the feed is constrained due to workpiece flexibility, which can cause chatter. Also, in an operation such as face milling, the flexibility of the workpiece fixture does not allow for high feed as the cutting speed increases.
High speed milling of titanium is limited because of the dynamic behavior of the tool/workpiece/fixture system and the loads on the tools. Vibration can occur if the tooth passing frequency (No. of flutes or inserts *spindle speedxe2x88x92rpm/60) matches the frequency of anyone component of the tool/workpiece/fixture system. This type of vibration is usually referred to as forced vibration.
With reference to FIG. 1, there is illustrated a mass experiencing a single degree of freedom under forced vibration excitation. The amplitude of motion depends upon both on the amplitude of the force and on the frequency of the force. A low frequency of excitation force causes a displacement determined by the familiar xe2x80x9cstaticxe2x80x9d stiffness (F=kx). As the excitation frequency increases, so does the amplitude of the displacement, up to the xe2x80x9cresonancexe2x80x9d. At resonance, the frequency of the excitation force matches the natural frequency. At resonance, the amplitude of the displacement is much larger than at low frequency. For excitation frequencies higher than the natural frequency, the amplitude of the displacement decreases. The forced vibration, as seen in FIG. 2, is termed as a Frequency Response Function (FRF), where xcfx89 is the frequency of the exciting force and xcfx89n is the natural frequency of the system. As illustrated, the figure on the right is a plot of the displacement occurring at the natural frequency while the plot on the left illustrates the different levels of displacement given a level of excitation wherein the maximum displacement occurs at the natural frequency. The natural frequency is represented as:
xcfx89n{square root over (k/m)},
Where k is the stiffness and m is the mass of the system.
In general, FIG. 2 shows that the Frequency Response Function (FRF) describes how a tool/workpiece/fixture system will vibrate in response to different frequencies of excitation. The FRF is a measurable function, and it can be used to compare and predict the performance of cutters and machine tools. There is a very high correlation between the FRF and the amount of speed and power that can be used in a milling operation.
Whereas xe2x80x9csingle degree of freedomxe2x80x9d systems have 1 natural frequency, xe2x80x9cmultiple degree of freedomxe2x80x9d systems have 1 natural frequency for each degree of freedom. Each natural frequency has a corresponding characteristic deformation pattern (mode shape). Vibration in xe2x80x9cmultiple degree of freedomxe2x80x9d systems may be thought of as a sum of vibrations in the individual modes.
With reference to FIG. 3, there is illustrated the wavy surface 31 produced on a workpiece 33 when a milling cutter or tool 35 makes a pass resulting from the tooth passing frequency. When a subsequent pass is made, the cutter 35 removes material from an existing wavy surface and at the same time leaves behind a new wavy surface. The regeneration of waviness causes a steady input of energy from the milling spindle drive into vibration at the cutting edge. The chip that is created by this cut carries both the waviness from the previous pass and that translated over by the current pass.
If the new cut leads to a chip with constant thickness (i.e. the waviness of the chip is in phase), it creates a stable cut as illustrated in FIG. 4. If the waviness generates variable chip thickness (i.e. the waves are out of phase as illustrated in FIG. 5), this translates as variable forces on the cutting edge and eventually as vibration. This leads to the most undesirable vibrations in milling, specifically, self-excited chatter vibrations.
Chatter, the self-excited vibration between the workpiece 33 and the cutting tool, is another common problem during high speed machining and titanium. It significantly limits the machining productivity, adversely affects the surface quality, accelerates the premature failure of cutting tools, and damages the machine tool components. In general, it is observed that chatter cannot occur at the tooth passing frequency or any of its harmonics because there is no regeneration. This statement is correct if the tool is the most flexible part in the system. In high speed machining of titanium, the natural frequency of the workpiece and its system affect to a great extent the chatter generation condition.
A number of different strategies have been used to increase the stability, and thus productivity, of the machining system. These include increasing the rigidity and damping characteristics of the structure, selecting cutting conditions such as feed rate and spindle speed and the use of other schemes like Variable Speed Machining (VSM) wherein the nominal spindle speed varies continuously (typically along a sinusoidal trajectory) during machining.
For a given machine tool structure, the stability of the system can be enhanced by the proper selection of constant spindle speed using both off-line and on-line methods. In an effort to select cutting conditions that provide stable machining and high productivity, researchers have developed engineering tools commonly referred to as xe2x80x9cstability chartsxe2x80x9d. These charts generally show that as the spindle speed increases, wider speed intervals are developed within which relatively large depths of cut can be achieved while maintaining stability. This will increase the rate of metal removal. The stability of the system is obtained by repeatedly running the simulations at different combinations of spindle speed and depth of cut until the system becomes unstable.
Recently, a few analytical methods to predict the stability of Constant Spindle Speed Machining (CSM) have been developed. An iterative analytical stability model for determining the chatter stability for machining with a variable pitch cutter using constant spindle speed has been developed. In addition, in most reports, the machining chatter is modeled as a linear differential-difference equation with single regenerative effects. In reality, when chatter occurs, the amplitude of self-excited vibration increases until some non-linear effect limits any further increment. The stability analysis of linear models provides information only about the chatter threshold, but gives no information about the system behavior after the stability borderline has been exceeded. However, the information related to chatter after the stability borderline has been exceeded is of importance for the effective speed.
Aluminum is often machined in such a manner that the tooth passing frequency is equal to the natural frequency of the cutting tool. Cutting at the natural frequency of the tool indicates that the phase shift between the periodic excitation acting on the machine system due to the tooth passing frequency and displacement history of the machine-tool-work is equal to zero. This minimizes the magnitude of the real part of the system transfer function.
It is therefore possible to successfully utilize the above-mentioned technology for determining the optimum cutting speed for high speed machining of aluminum. However, it is difficult to apply the same technology for high speed machining of titanium alloy. The predicted stable depth of cut is too small to be used in practical cases. The dynamic force components in the case of machining titanium is about 30% of that generated during the machining of steel alloy or aluminum. Therefore, keeping the phase difference at zero degrees does not have a great effect on the amplitude of the undulation that is generated on the surface.
In addition, the use of active control technology is becoming more and more a routine application for aircraft systems. Active control schemes for vibration have long been studied, including fixed-frame swashplate control (higher harmonic control), rotating frame blade control (individual blade control, active flap control, active blade twist control), active transmission isolation (active transmission mounts, active control of structural response (ACSR)), and so on. Active control technology is also resident in other systems on the aircraft, for example flight controls, and is becoming more robust and expansive in functionality due to improvements and proliferation of digital capabilities throughout the aircraft system.
Much of the basic system dynamics and control strategies, in a generic sense, are applicable to the manufacturing process as well. There are many limitations in the manufacturing process today, whether cutting speed, depth, feed, etc., that arise due to dynamic constraints as noted above. Specifically, the cutting tool and the part to be cut are both dynamic systems. Further, during the cutting process, these systems exhibit changing dynamic characteristics. In whole, this coupled dynamic system exhibits resonances and modes that must be avoided to yield adequate quality in the resultant part. There is therefore needed a method of applying some of the basic tenants of active control to augment the manufacturing process and yield improved quality parts in less time and at less cost.
Such a methodology would ideally be approached via several levels of complexity with associated levels of productivity increase. Historically, the task has been one of xe2x80x9cgo as fast as you canxe2x80x9d until the quality begins to degrade, then back off a bit to keep the quality adequate. This process, obviously, is ad hoc, and precludes the identification of optimum operating regimes.
It would be preferable if a methodology were to be employed which could account for the changing dynamics of the tool and part as the cutting operation progresses. What is therefore needed is a simple systematic technique to define the stable high cutting speed in machining titanium and which takes into account the changing dynamics of the tool and part as the cutting operation progresses.
Accordingly, it is an object of the present invention to provide a method for the systematic prediction of stable high speed cutting parameters for machining titanium.
In accordance with the present invention, a method of predicting the cutting speed for machining of titanium alloy comprises the steps of obtaining a first transfer function for a tool system, obtaining a second transfer function for a workpiece system, selecting from the first transfer function a first flexible mode, selecting from the second transfer function a second flexible mode, defining a natural frequency of the first flexible mode and the second flexible mode, calculating a tooth passing frequency using the defined natural frequency, accepting the calculated tooth passing frequency if the calculated tooth passing frequency differs from a second harmonic of a combined system formed of the tool system and the workpiece system and from at least one natural frequency corresponding to the tool system and the workpiece system, calculating a stable spindle speed, defining a cut depth using the calculated spindle speed.
Alternatively, in accordance with the present invention, a method is provided whereby dynamic characterization followed by addition of sensors and actuating elements to control part and/or tool dynamics via a closed feedback processing system yield freedom to select speed, feed and cutting depth to optimize tool use and part manufacturing and avoid the need to work around tool and part dynamic constraints.